A "Conjecture" is a big fancy word for a "guess", usually for something that is probably true without a proof. The Twin Prime Conjecture is one of these oldest guesses ever known. A twin prime are two numbers with difference of 2 that are both primes. For example, 3 and 5, 11 and 13, 41 and 43, etc.
The guess is: is there infinitely many such pairs?
This is one of those simple-to-state, but hard-to-prove-or-disprove statement.
Euclid already proved that there are infinitely many primes (with a remarkable proof by contradiction). Chances are: there are infinitely many twin primes, but no one can say for certain.
Dry and boring you say? I found a great entertaining song!
http://www.pbs.org/wgbh/nova/sciencenow/3302/02.html
If presented right, math can even be an entertaining subject!
What does it matter if there are infinite or finitely many twin primes? Answer: Curiousity demands answers.
Hmm, let me start with the similar fashion as Euclid: let p and p+2 be the last set of twin primes... if I can find another set of twin primes beyond that, or another contradiction then I've got it!
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